Yet, there is a fourth way, which for an academic is more controversial. If Harvard increased the teaching load of the economics faculty, this would reduce the student to faculty ratio. Now, I understand why Mankiw did not advocate higher teaching loads - doing so would increase the overall work load of faculty, and not many are advocating working more for the same salary. Yet, if the goal is to reduce student-faculty ratios, this would be the most budget nuetral.
As someone who teaches a 4-4 load*, I got a kick out of this post. Seriously, though, I've taught Principles classes to class sizes as small as 30 all the way up to an enrollment of 500**. I've taught what amounts to Intermediate Micro in classes ranging from 80 - 200 students. Most of my Principles classes nowadays are right around 50 or so, and I can't imagine that there' much of a difference between teaching 3 classes of 50 each or 2 classes of 75 each. There's probably a barrier, maybe between 80-100 students, where class size gets in the way of class discussion (in that the sheer size of the class drives students to be quiet who would be more likely to talk in a smaller class).
So, what is the optimal class size?
*I teach an MBA course in the spring semester that lasts for 8 weeks, but because it is a grad course it counts as a full class.
Faculty also usually have the chance to get research reassignments in which faculty work on a research reassignment in exchange for not teaching a class. I've received three of them so far. Here's one paper that came from one of those assignments. I gave a lecture based on the same paper a few years back. Here's a pub from the second one. The third paper is currently under revision for a resubmission.
**I tailgate at Mizzou games with two former students from that 500-seat lecture course. I know one of them told me that he didn't come to class much. I told him that it was no skin off my back because I wouldn't have noticed him anyways. When he first introduced himself to me I thought "I have no idea who you are."